Does fresnel node corresponds to fresnel-equations?
First,the answer is yes.In most occasions you don't need to worry about reflection amount when using fresnel as fac in mixing shader.
Second,the fresnel equation compeletely characterizes reflection and refraction in a transmissive surface.In blender,the light is treated as unpolarized so that the reflection amount is 1/2*(R_s+R_p).Theoretically,the fresnel node should be used as fac for mixing refraction and reflection.Diffuse is an approximation of subsurface scattering,so for some materials we assume the refracted light is all scattered so we can replace refraction  shader by diffuse shader.